At least one Palestinian was injured when an Israeli airstrike hit a group of militants in eastern Gaza City, medics and witnesses said.
Witnesses reported seeing militants trying to fire rockets into southern Israel shortly before the strike, which was mounted by an Israeli drone and hit the eastern Shejaiya district that lies close to the border.
Earlier, witnesses said two Palestinians were injured by Israeli tank fire in the same area in an incident which occurred shortly after a rocket was fired into Israel, causing no injuries or damage.
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The latest unrest follows days of rising cross-border violence, which has ramped up tensions between the Israeli military and Gaza's Islamist Hamas rulers and once again raised fears of a large-scale Israeli invasion to stamp out rocket fire.
Overnight, Israel staged multiple air raids in Gaza, wounding 17 people, most of them lightly, two days after Hamas's armed wing, the Ezzedine al-Qassam Brigades, fired more than 50 mortars at the Jewish state, slightly injuring two people.
Palestinian medical sources two women and seven children were among those hurt in the overnight raids which Israel said had hit "terror tunnels," weapons factories and various other sites.
Several hours before the Israeli attack, the Ezzedine al-Qassam Brigades had offered to stop the rocket firing if Israel would end its attacks on Gaza.
It said Saturday's barrage of 50 or so projectiles had been in response to an Israeli strike the previous Wednesday which killed two of its members.
That strike was launched in broad daylight immediately after a mortar shell fell in southern Israel, causing no injuries or damage in what some commentators criticised as a disproportionate response.
Saturday's mortar attacks represented the most intensive bombardment since Israel's 22-day war on Gaza, which ended on January 18, 2009 and killed 1,400 Palestinians, more than half of them civilians, and 13 Israelis, 10 of them soldiers.
